# Geostationary orbit

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A geostationary orbit, often referred to as a geosynchronous equatorial orbit [1] (GEO), is a circular geosynchronous orbit 35,786 km (22,236 mi) above Earth's equator and following the direction of Earth's rotation. An object in such an orbit appears motionless, at a fixed position in the sky, to ground observers. Communications satellites and weather satellites are often placed in geostationary orbits, so that the satellite antennae (located on Earth) that communicate with them do not have to rotate to track them, but can be pointed permanently at the position in the sky where the satellites are located. Using this characteristic, ocean-color monitoring satellites with visible and near-infrared light sensors (e.g. GOCI) can also be operated in geostationary orbit in order to monitor sensitive changes of ocean environments.

A circular orbit is the orbit with a fixed distance around the barycenter, that is, in the shape of a circle.

A geosynchronous orbit is an orbit around Earth of a satellite with an orbital period that matches Earth's rotation on its axis, which takes one sidereal day. The synchronization of rotation and orbital period means that, for an observer on Earth's surface, an object in geosynchronous orbit returns to exactly the same position in the sky after a period of one sidereal day. Over the course of a day, the object's position in the sky traces out a path, typically in a figure-8 form, whose precise characteristics depend on the orbit's inclination and eccentricity. Satellites are typically launched in an eastward direction. A geosynchronous orbit is 35,786 km (22,236 mi) above the Earth's surface. Those closer to Earth orbit faster than Earth rotates, so from Earth, they appear to move eastward while those that orbit beyond geosynchronous distances appear to move westward.

Earth is the third planet from the Sun and the only astronomical object known to harbor life. According to radiometric dating and other sources of evidence, Earth formed over 4.5 billion years ago. Earth's gravity interacts with other objects in space, especially the Sun and the Moon, Earth's only natural satellite. Earth revolves around the Sun in 365.26 days, a period known as an Earth year. During this time, Earth rotates about its axis about 366.26 times.

## Contents

A geostationary orbit is a particular type of geosynchronous orbit, which has an orbital period equal to Earth's rotational period, or one sidereal day (23 hours, 56 minutes, 4 seconds). Thus, the distinction is that, while an object in geosynchronous orbit returns to the same point in the sky at the same time each day, an object in geostationary orbit never leaves that position. Geosynchronous orbits move around relative to a point on Earth's surface because, while geostationary orbits have an inclination of 0° with respect to the Equator, geosynchronous orbits have varying inclinations and eccentricities.

The orbital period is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars.

Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.

An equator of a rotating spheroid is its zeroth circle of latitude (parallel). It is the imaginary line on the spheroid's surface, equidistant from its poles, dividing it into northern and southern hemispheres. In other words, it is the intersection of the spheroid's surface with the plane perpendicular to its axis of rotation and midway between its geographical poles.

## History

The first appearance of a geostationary orbit in popular literature was in the first Venus Equilateral story by George O. Smith, [2] but Smith did not go into details. British science fiction author Arthur C. Clarke disseminated the idea widely, with more details on how it would work, in a 1945 paper entitled "Extra-Terrestrial Relays — Can Rocket Stations Give Worldwide Radio Coverage?", published in Wireless World magazine. Clarke acknowledged the connection in his introduction to The Complete Venus Equilateral. [3] The orbit, which Clarke first described as useful for broadcast and relay communications satellites, [4] is sometimes called the Clarke Orbit. [5] Similarly, the Clarke Belt is the part of space about 35,786 km (22,236 mi) above sea level, in the plane of the equator, where near-geostationary orbits may be implemented. The Clarke Orbit is about 265,000 km (165,000 mi) in circumference.

The Venus Equilateral series is a set of 13 science fiction short stories by American writer George O. Smith, concerning the Venus Equilateral Relay Station, an interplanetary communications hub located at the L4 Lagrangian point of the Sun-Venus system. Most of the stories were first published in Astounding Science Fiction between 1942 and 1945.

George Oliver Smith was an American science fiction author. He is not to be confused with George H. Smith, another American science fiction author.

Sir Arthur Charles Clarke was a British science fiction writer, science writer and futurist, inventor, undersea explorer, and television series host.

## Practical uses

Most commercial communications satellites, broadcast satellites and SBAS satellites operate in geostationary orbits. A geostationary transfer orbit is used to move a satellite from low Earth orbit (LEO) into a geostationary orbit. The first satellite placed into a geostationary orbit was the Syncom-3, launched by a Delta D rocket in 1964.

A communications satellite is an artificial satellite that relays and amplifies radio telecommunications signals via a transponder; it creates a communication channel between a source transmitter and a receiver at different locations on Earth. Communications satellites are used for television, telephone, radio, internet, and military applications. There are 2,134 communications satellites in Earth’s orbit, used by both private and government organizations. Many are in geostationary orbit 22,200 miles (35,700 km) above the equator, so that the satellite appears stationary at the same point in the sky, so the satellite dish antennas of ground stations can be aimed permanently at that spot and do not have to move to track it.

A low Earth orbit (LEO) is an Earth-centered orbit with an altitude of 2,000 km (1,200 mi) or less, or with at least 11.25 periods per day and an eccentricity less than 0.25. Most of the manmade objects in space are in LEO. A histogram of the mean motion of the cataloged objects shows that the number of objects drops significantly beyond 11.25.

Syncom started as a 1961 NASA program for active geosynchronous communication satellites, all of which were developed and manufactured by Hughes Space and Communications. Syncom 2, launched in 1963, was the world's first geosynchronous communications satellite. Syncom 3, launched in 1964, was the world's first geostationary satellite.

A worldwide network of operational geostationary meteorological satellites is used to provide visible and infrared images of Earth's surface and atmosphere. These satellite systems include:

The Meteosat series of satellites are geostationary meteorological satellites operated by EUMETSAT under the Meteosat Transition Programme (MTP) and the Meteosat Second Generation (MSG) program.

The European Space Agency is an intergovernmental organisation of 22 member states dedicated to the exploration of space. Established in 1975 and headquartered in Paris, France, ESA has a worldwide staff of about 2,200 in 2018 and an annual budget of about €5.72 billion in 2019.

Japan is an island country in East Asia. Located in the Pacific Ocean, it lies off the eastern coast of the Asian continent and stretches from the Sea of Okhotsk in the north to the East China Sea and the Philippine Sea in the south.

A statite, a hypothetical satellite that uses a solar sail to modify its orbit, could theoretically hold itself in a geostationary "orbit" with different altitude and/or inclination from the "traditional" equatorial geostationary orbit. [6]

A statite is a hypothetical type of artificial satellite that employs a solar sail to continuously modify its orbit in ways that gravity alone would not allow. Typically, a statite would use the solar sail to "hover" in a location that would not otherwise be available as a stable geosynchronous orbit. Statites have been proposed that would remain in fixed locations high over Earth's poles, using reflected sunlight to counteract the gravity pulling them down. Statites might also employ their sails to change the shape or velocity of more conventional orbits, depending upon the purpose of the particular statite.

Solar sails are a proposed method of spacecraft propulsion using radiation pressure exerted by sunlight on large mirrors. A useful analogy may be a sailing boat; the light exerting a force on the mirrors is akin to a sail being blown by the wind. High-energy laser beams could be used as an alternative light source to exert much greater force than would be possible using sunlight, a concept known as beam sailing.

### Communications

Satellites in geostationary orbits are far enough away from Earth that communication latency becomes significant — about a quarter of a second for a trip from one ground-based transmitter to the satellite and back to another ground-based transmitter; close to half a second for a round-trip communication from one Earth station to another and then back to the first.

For example, for ground stations at latitudes of φ = ±45° on the same meridian as the satellite, the time taken for a signal to pass from Earth to the satellite and back again can be computed using the cosine rule, given the geostationary orbital radius r (derived below), the Earth's radius R and the speed of light c, as

${\displaystyle \Delta t={\frac {2}{c}}{\sqrt {R^{2}+r^{2}-2Rr\cos \varphi }}\approx 253~{\text{ms}}.}$

(Note that r is the orbital radius, the distance from the centre of the Earth, not the height above the equator.)

This delay presents problems for latency-sensitive applications such as voice communication. [7]

Geostationary satellites are directly overhead at the equator and appear lower in the sky to an observer nearer the poles. As the observer's latitude increases, communication becomes more difficult due to factors such as atmospheric refraction, Earth's thermal emission, line-of-sight obstructions, and signal reflections from the ground or nearby structures. At latitudes above about 81°, geostationary satellites are below the horizon and cannot be seen at all. [8] Because of this, some Russian communication satellites have used elliptical Molniya and Tundra orbits, which have excellent visibility at high latitudes.

### Orbit allocation

Satellites in geostationary orbit must all occupy a single ring above the equator. The requirement to space these satellites apart to avoid harmful radio-frequency interference during operations means that there are a limited number of orbital "slots" available, and thus only a limited number of satellites can be operated in geostationary orbit. This has led to conflict between different countries wishing access to the same orbital slots (countries near the same longitude but differing latitudes) and radio frequencies. These disputes are addressed through the International Telecommunication Union's allocation mechanism. [9] [10] In the 1976 Bogotá Declaration, eight countries located on the Earth's equator claimed sovereignty over the geostationary orbits above their territory, but the claims gained no international recognition. [11]

## Orbital stability

A geostationary orbit can be achieved only at an altitude very close to 35,786 km (22,236 mi) and directly above the equator. This equates to an orbital velocity of 3.07 km/s (1.91 mi/s) and an orbital period of 1,436 minutes, which equates to almost exactly one sidereal day (23.934461223 hours). This ensures that the satellite will match the Earth's rotational period and has a stationary footprint on the ground. All geostationary satellites have to be located on this ring.

A combination of lunar gravity, solar gravity, and the flattening of the Earth at its poles causes a precession motion of the orbital plane of any geostationary object, with an orbital period of about 53 years and an initial inclination gradient of about 0.85° per year, achieving a maximal inclination of 15° after 26.5 years. [12] To correct for this orbital perturbation, regular orbital stationkeeping maneuvers are necessary, amounting to a delta-v of approximately 50 m/s per year.

A second effect to be taken into account is the longitudinal drift, caused by the asymmetry of the Earth – the equator is slightly elliptical. There are two stable (at 75.3°E and 252°E) and two unstable (at 165.3°E and 14.7°W) equilibrium points. Any geostationary object placed between the equilibrium points would (without any action) be slowly accelerated towards the stable equilibrium position, causing a periodic longitude variation. [12] The correction of this effect requires station-keeping maneuvers with a maximal delta-v of about 2 m/s per year, depending on the desired longitude.

Solar wind and radiation pressure also exert small forces on satellites; over time, these cause them to slowly drift away from their prescribed orbits.

In the absence of servicing missions from the Earth or a renewable propulsion method, the consumption of thruster propellant for station keeping places a limitation on the lifetime of the satellite. Hall-effect thrusters, which are currently in use, have the potential to prolong the service life of a satellite by providing high-efficiency electric propulsion.

### Limitations to usable life of geostationary satellites

When they run out of thruster fuel, the satellites are at the end of their service life, as they are no longer able to stay in their allocated orbital position. The transponders and other onboard systems generally outlive the thruster fuel and, by stopping N–S station keeping, some satellites can continue to be used in inclined orbits (where the orbital track appears to follow a figure-eight loop centred on the equator), [13] [14] or else be elevated to a "graveyard" disposal orbit.

## Derivation of geostationary altitude

In any circular orbit, the centripetal force required to maintain the orbit (Fc) is provided by the gravitational force on the satellite (Fg). To calculate the geostationary orbit altitude, one begins with this equivalence:

${\displaystyle \mathbf {F} _{\text{c}}=\mathbf {F} _{\text{g}}.}$

By Newton's second law of motion, [15] we can replace the forces F with the mass m of the object multiplied by the acceleration felt by the object due to that force:

${\displaystyle m\mathbf {a} _{\text{c}}=m\mathbf {g} .}$

We note that the mass of the satellite m appears on both sides — geostationary orbit is independent of the mass of the satellite. [lower-alpha 3] Calculating the geostationary altitude, therefore, simplifies down to calculating the altitude where the magnitudes of the centripetal acceleration required for orbital motion and the gravitational acceleration provided by Earth's gravity are equal.

The centripetal acceleration's magnitude is:

${\displaystyle |\mathbf {a} _{\text{c}}|=\omega ^{2}r,}$

where ω is the angular speed, and r is the orbital geocentric radius (measured from the Earth's center of mass).

The magnitude of the gravitational acceleration is:

${\displaystyle |\mathbf {g} |={\frac {GM}{r^{2}}},}$

where M is the mass of Earth, 5.9736 × 1024 kg, and G is the gravitational constant, (6.67428 ± 0.00067) × 10−11 m3 kg−1 s−2.

Equating the two accelerations gives:

${\displaystyle r^{3}={\frac {GM}{\omega ^{2}}}\to r={\sqrt[{3}]{\frac {GM}{\omega ^{2}}}}.}$

The product GM is known with much greater precision than either factor alone; it is known as the geocentric gravitational constant μ = 398,600.4418 ± 0.0008 km3 s−2. Hence

${\displaystyle r={\sqrt[{3}]{\frac {\mu }{\omega ^{2}}}}}$

The angular speed ω is found by dividing the angle travelled in one revolution (360° = 2π rad) by the orbital period (the time it takes to make one full revolution). In the case of a geostationary orbit, the orbital period is one sidereal day, or 86164.09054 s). [16] This gives

${\displaystyle \omega \approx {\frac {2\pi ~{\text{rad}}}{86\,164~{\text{s}}}}\approx 7.2921\times 10^{-5}~{\text{rad/s}}.}$

The resulting orbital radius is 42,164 kilometres (26,199 mi). Subtracting the Earth's equatorial radius, 6,378 kilometres (3,963 mi), gives the altitude of 35,786 kilometres (22,236 mi).

Orbital speed is calculated by multiplying the angular speed by the orbital radius:

${\displaystyle v=\omega r\approx 3.0746~{\text{km/s}}\approx 11\,068~{\text{km/h}}\approx 6877.8~{\text{mph}}.}$

By the same formula, we can find the geostationary-type orbit of an object in relation to Mars (this type of orbit above is referred to as an areostationary orbit if it is above Mars). The geocentric gravitational constant GM (which is μ) for Mars has the value of 42,828 km3s−2, and the known rotational period (T) of Mars is 88,642.66 seconds. Since ω = 2π/T, using the formula above, the value of ω is found to be approx 7.088218×10−5 s−1. Thus r3 = 8.5243×1012 km3, whose cube root is 20,427 km (the orbital radius); subtracting the equatorial radius of Mars (3396.2 km) gives the orbital altitude of 17,031 km.

Orbital speed of a Mars geostationary orbit can be calculated as for Earth above:

${\displaystyle v=\omega r\approx 1.4479~{\text{km/s}}\approx 5\,212~{\text{km/h}}\approx 3238~{\text{mph}}.}$

## Notes

1. Orbital periods and speeds are calculated using the relations 4π²R³ = T²GM and V²R = GM, where R = radius of orbit in metres, T = orbital period in seconds, V = orbital speed in m/s, G = gravitational constant 6.673×1011 Nm²/kg², M = mass of Earth 5.98×1024 kg.
2. Approximately 8.6 times when the moon is nearest (363104 km ÷ 42164 km) to 9.6 times when the moon is farthest (405,696 km ÷ 42,164 km).
3. In the small-body approximation, the geostationary orbit is independent of the satellite's mass. For satellites having a mass less than M μerr/μ ≈ 1015 kg, that is, over a billion times that of the ISS, the error due to the approximation is smaller than the error on the universal geocentric gravitational constant (and thus negligible).

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This article incorporates  public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MIL-STD-188 ).